We develop a theoretical and computational model to investigate the ballistic response of
a hybrid two-layered flexible armor system. In particular, we study the effects of stacking
order of the two fibrous layers, which have distinctly different mechanical properties, on
the
limit
velocity. A system consisting of Kevlar and Spectra fabrics is studied in detail. For this
system, previous experimental results of Cunniff show nearly a factor of two difference in
the
velocities for the two possible stacking orders. The new model presented here extends
our previous multilayer model by directly addressing interference effects between the
two layers, treated here using length and tension compatibility along the
radial direction away from the projectile. The primary task is to calculate
strains in the individual layers in the presence of constraining interference
that forces the nested layers to have a common impact cone shape different
from what would be generated by the impact if the layers were allowed to
deform freely. We show that this interference, together with relative areal
densities of the layers, have a significant effect on the strain evolution in the
layers, particularly near the edge of the projectile where failure initiates. As
observed experimentally by Cunniff, our model predicts a large decrease in the
velocity of the hybrid armor system when Spectra is the strike layer. However, to
achieve this reduction it is necessary to use a lowered normalization velocity in
multilayered Spectra systems than the theoretical value obtained from basic fiber
properties. Besides matching the experimental results of Cunniff, the model reveals
many subtle transitions in the onset and effects of interference between the layers.
Somewhat surprising and contrary to conventional wisdom is the observation that
layer interference can sometimes be beneficial depending on the relative mechanical
properties and areal densities of the two layers.
